We show the existence of a smooth spherical surface minimizing the Willmore functional subject to an area constraint in a compact Riemannian three-manifold, provided the area is small enough. Moreover, we partially classify complete surfaces of Willmore type with positive mean curvature in Riemannian three-manifolds.
@article{AIHPC_2013__30_3_497_0,
author = {Lamm, Tobias and Metzger, Jan},
title = {Minimizers of the {Willmore} functional with a small area constraint},
journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
pages = {497--518},
publisher = {Elsevier},
volume = {30},
number = {3},
year = {2013},
doi = {10.1016/j.anihpc.2012.10.003},
zbl = {1290.49090},
language = {en},
url = {http://archive.numdam.org/articles/10.1016/j.anihpc.2012.10.003/}
}
TY - JOUR AU - Lamm, Tobias AU - Metzger, Jan TI - Minimizers of the Willmore functional with a small area constraint JO - Annales de l'I.H.P. Analyse non linéaire PY - 2013 SP - 497 EP - 518 VL - 30 IS - 3 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.anihpc.2012.10.003/ DO - 10.1016/j.anihpc.2012.10.003 LA - en ID - AIHPC_2013__30_3_497_0 ER -
%0 Journal Article %A Lamm, Tobias %A Metzger, Jan %T Minimizers of the Willmore functional with a small area constraint %J Annales de l'I.H.P. Analyse non linéaire %D 2013 %P 497-518 %V 30 %N 3 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.anihpc.2012.10.003/ %R 10.1016/j.anihpc.2012.10.003 %G en %F AIHPC_2013__30_3_497_0
Lamm, Tobias; Metzger, Jan. Minimizers of the Willmore functional with a small area constraint. Annales de l'I.H.P. Analyse non linéaire, Tome 30 (2013) no. 3, pp. 497-518. doi : 10.1016/j.anihpc.2012.10.003. http://archive.numdam.org/articles/10.1016/j.anihpc.2012.10.003/
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